In order to perform computations we will use a technique known as method of regionsSee [1]} for a comprehensive review in the context of SCET. which allows us to carry out asymptotic expansions of loop integrals [2]} in dimensional regularization around various limits [3]}. The expansion is obtained by splitting the integration in different regions and by expanding the integrand in each case. In the effective field theory approach, the different regions will be represented by different effective theory fields. The expanded integrals obtained by means of the strategy of regions technique are in one-to-one correspondence to Feynman diagrams of effective field theories regularized in dimensional regularization. If one is simply interested to expand some perturbative result in a small parameter, one can use the strategy of regions without the need of an effective Lagrangian. However, the use of an effective field theory offers some important advantages when one is interested in deriving all-order statements, like factorization theorems or to resum logarithmic contributions at all orders in the coupling constants using Renormalization Group (RG) techniques.
In addition, in the EFT gauge invariant is manifest at the Lagrangian level, while this is not true for individual diagrams. The effective Lagrangian also provides a systematic way to organize higher power corrections, by including subleading terms in the effective Lagrangian.
